We have recently run into some questionable behavior on Mathoverflow: occasional users asked a question, it received a valid answer, and then the question was deleted immediately before the answer had time to gather upvotes. In one case we guess that it is because the poster found the question embarrassingly simple in retrospect, in the other there was clearly some malicious intent (plagiarism).
Anyways, it looks like this is a bad habit that should be forbidden, because those answers require time to write, and it is value that goes lost to all other users.
The current policy is that the asker can delete their own question (and its associated answers) as long as there is at most one answer with no upvotes.
One possible fix would be disallowing deletion of answered questions altogether, irrespective of their score. Another fix would be allowing deletion only after a certain time since the last posted answer, like a couple of days. In this way, good answers have some time to gather upvotes.
changing the condition so that the question can be deleted only if it has an answer with
score < 0is not a fix, because the asker can downvote the answer and then delete. Changing it to
score < 3, for instance, would encourage sock-puppeting, and reduce a lot the cases when this rule is applicable.
the asker has no legal right to have their own question deleted, because they licensed it to SE under a CC license and they cannot take away this license once it has been granted. I see no moral obligations either.
It is particularly hard to catch this behavior after the question has been deleted, because deleted questions have very low visibility currently (they only appear as a link in the moderator queue, I believe?).